The Pseudo-Hyperbolic Functions and the Matrix Representation of Eisenstein Complex Numbers
G. Dattoli, E.Sabia, M. Del Franco
TL;DR
This paper explores the matrix representation of Eisenstein numbers and introduces Pseudo Hyperbolic Functions, providing a geometric interpretation and demonstrating their application in physical problems like light scattering by crystals.
Contribution
It develops a new matrix-based approach to Eisenstein numbers and introduces Pseudo Hyperbolic Functions with a geometric perspective, linking mathematical theory to physical phenomena.
Findings
Matrix representation of Eisenstein numbers is effective
Pseudo Hyperbolic Functions have useful geometric interpretations
Application demonstrated in light scattering by crystals
Abstract
We consider the matrix representation of the Eisenstein numbers and in this context we discuss the theory of the Pseudo Hyperbolic Functions. We develop a geometrical interpretation and show the usefulness of the method in Physical problems related to the anomalous scattering of light by crystals
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Mathematics and Applications